Relevant bibliographies by topics / Manifolds (Mathematics) Nonlinear theories

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Academic literature on the topic 'Manifolds (Mathematics) Nonlinear theories'

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Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Manifolds (Mathematics) Nonlinear theories"

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Nigsch, E. A., and J. A. Vickers. "Nonlinear generalized functions on manifolds." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476, no. 2244 (December 2020): 20200640. http://dx.doi.org/10.1098/rspa.2020.0640.

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In this work, we adopt a new approach to the construction of a global theory of algebras of generalized functions on manifolds based on the concept of smoothing operators. This produces a generalization of previous theories in a form which is suitable for applications to differential geometry. The generalized Lie derivative is introduced and shown to extend the Lie derivative of Schwartz distributions. A new feature of this theory is the ability to define a covariant derivative of generalized scalar fields which extends the covariant derivative of distributions at the level of association. We end by sketching some applications of the theory. This work also lays the foundations for a nonlinear theory of distributional geometry that is developed in a subsequent paper that is based on Colombeau algebras of tensor distributions on manifolds.
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Avramidi, Ivan G., and Giampiero Esposito. "Gauge Theories on Manifolds with Boundary." Communications in Mathematical Physics 200, no. 3 (February 1, 1999): 495–543. http://dx.doi.org/10.1007/s002200050539.

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Dimofte, Tudor, Davide Gaiotto, and Sergei Gukov. "Gauge Theories Labelled by Three-Manifolds." Communications in Mathematical Physics 325, no. 2 (December 15, 2013): 367–419. http://dx.doi.org/10.1007/s00220-013-1863-2.

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Wei, Shihsuh Walter. "The balance between existence and nonexistence theorems in differential geometry." Tamkang Journal of Mathematics 32, no. 1 (March 31, 2001): 61–88. http://dx.doi.org/10.5556/j.tkjm.32.2001.370.

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We discuss the delicate balance between existence and nonexistence theorems in differential geometry. Studying their interplay yields some information about $ p $-harmonic maps, $ p $-SSU manifolds, geometric $ k_p $-connected manifolds, minimal hypersurfaces and Gauss maps, and manifolds admitting essential positive supersolutions of certain nonlinear PDE. As an application of the theory developed, we obtain a topological theorem for minimal submanifolds in complete manifolds with nonpositive sectional curvature.
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Monnier, Samuel. "Topological field theories on manifolds with Wu structures." Reviews in Mathematical Physics 29, no. 05 (April 12, 2017): 1750015. http://dx.doi.org/10.1142/s0129055x17500155.

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We construct invertible field theories generalizing abelian prequantum spin Chern–Simons theory to manifolds of dimension [Formula: see text] endowed with a Wu structure of degree [Formula: see text]. After analyzing the anomalies of a certain discrete symmetry, we gauge it, producing topological field theories whose path integral reduces to a finite sum, akin to Dijkgraaf–Witten theories. We take a general point of view where the Chern–Simons gauge group and its couplings are encoded in a local system of integral lattices. The Lagrangian of these theories has to be interpreted as a class in a generalized cohomology theory in order to obtain a gauge invariant action. We develop a computationally friendly cochain model for this generalized cohomology and use it in a detailed study of the properties of the Wu Chern–Simons action. In the 3-dimensional spin case, the latter provides a definition of the “fermionic correction” introduced recently in the literature on fermionic symmetry protected topological phases. In order to construct the state space of the gauged theories, we develop an analogue of geometric quantization for finite abelian groups endowed with a skew-symmetric pairing. The physical motivation for this work comes from the fact that in the [Formula: see text] case, the gauged 7-dimensional topological field theories constructed here are essentially the anomaly field theories of the 6-dimensional conformal field theories with [Formula: see text] supersymmetry, as will be discussed elsewhere.
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Park, Jae-Suk. "Semi-Classical Quantum Fields Theories and Frobenius Manifolds." Letters in Mathematical Physics 81, no. 1 (June 21, 2007): 41–59. http://dx.doi.org/10.1007/s11005-007-0165-z.

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Cattaneo, Alberto S., Pavel Mnev, and Nicolai Reshetikhin. "Perturbative Quantum Gauge Theories on Manifolds with Boundary." Communications in Mathematical Physics 357, no. 2 (December 5, 2017): 631–730. http://dx.doi.org/10.1007/s00220-017-3031-6.

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SONG, YI, and STEPHEN P. BANKS. "DYNAMICAL SYSTEMS ON THREE MANIFOLDS PART II: THREE-MANIFOLDS, HEEGAARD SPLITTINGS AND THREE-DIMENSIONAL SYSTEMS." International Journal of Bifurcation and Chaos 17, no. 06 (June 2007): 2085–95. http://dx.doi.org/10.1142/s0218127407018233.

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The global behavior of nonlinear systems is extremely important in control and systems theory since the usual local theories will only provide information about a system in some neighborhood of an operating point. Away from that point, the system may have totally different behavior and so the theory developed for the local system will be useless for the global one. In this paper we shall consider the analytical and topological structure of systems on two- and three-manifolds and show that it is possible to obtain systems with "arbitrarily strange" behavior, i.e. arbitrary numbers of chaotic regimes which are knotted and linked in arbitrary ways. We shall do this by considering Heegaard Splittings of these manifolds and the resulting systems defined on the boundaries.
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Wu, Siye. "Topological quantum field theories on manifolds with a boundary." Communications in Mathematical Physics 136, no. 1 (February 1991): 157–68. http://dx.doi.org/10.1007/bf02096795.

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Dung, Nguyen Thac, Pham Duc Thoan, and Nguyen Dang Tuyen. "Liouville theorems for nonlinear elliptic equations on Riemannian manifolds." Journal of Mathematical Analysis and Applications 496, no. 1 (April 2021): 124803. http://dx.doi.org/10.1016/j.jmaa.2020.124803.

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Dissertations / Theses on the topic "Manifolds (Mathematics) Nonlinear theories"

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Gashler, Mike. "Manifold sculpting /." Diss., CLICK HERE for online access, 2007. http://contentdm.lib.byu.edu/ETD/image/etd1828.pdf.

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Vorpe, Katherine. "Understanding a Population Model for Mussel-Algae Interaction." Wittenberg University Honors Theses / OhioLINK, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=wuhonors1617970789779916.

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Lai, Mijia. "Fully nonlinear flows and Hessian equations on compact Kahler manifolds." Diss., University of Iowa, 2011. https://ir.uiowa.edu/etd/1010.

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In this thesis, we will study a class of fully nonlinear flows on Kähler manifolds. This family of flows generalizes the previously studied J-flow. We use the quotients of elementary symmetric polynomials or log of them to construct the flow. We obtain a necessary and sufficient condition in terms of positivity of certain cohomology class to guarantee the convergence of the flow. The corresponding limit metric gives rise to a critical metric satisfying a Hessian type equation on the manifold. We shall also discuss several geometric applications of our main result.
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West, Philip Davidson. "Nonlinear filtering for stochastic hybrid and nonlinear systems with applications to target tracking." Diss., Georgia Institute of Technology, 1994. http://hdl.handle.net/1853/14808.

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Guo, Sheng. "On Neumann Problems for Fully Nonlinear Elliptic and Parabolic Equations on Manifolds." The Ohio State University, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=osu1571696906482925.

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Conradie, Tanja. "Modelling of nonlinear dynamic systems : using surrogate data methods." Thesis, Stellenbosch : Stellenbosch University, 2000. http://hdl.handle.net/10019.1/51834.

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Thesis (MSc)--Stellenbosch University, 2000.
ENGLISH ABSTRACT: This study examined nonlinear modelling techniques as applied to dynamic systems, paying specific attention to the Method of Surrogate Data and its possibilities. Within the field of nonlinear modelling, we examined the following areas of study: attractor reconstruction, general model building techniques, cost functions, description length, and a specific modelling methodology. The Method of Surrogate Data was initially applied in a more conventional application, i.e. testing a time series for nonlinear, dynamic structure. Thereafter, it was used in a less conventional application; i.e. testing the residual vectors of a nonlinear model for membership of identically and independently distributed (i.i.d) noise. The importance of the initial surrogate analysis of a time series (determining whether the apparent structure of the time series is due to nonlinear, possibly chaotic behaviour) was illustrated. This study confrrmed that omitting this crucial step could lead to a flawed conclusion. If evidence of nonlinear structure in the time series was identified, a radial basis model was constructed, using sophisticated software based on a specific modelling methodology. The model is an iterative algorithm using minimum description length as the stop criterion. The residual vectors of the models generated by the algorithm, were tested for membership of the dynamic class described as i.i.d noise. The results of this surrogate analysis illustrated that, as the model captures more of the underlying dynamics of the system (description length decreases), the residual vector resembles Li.d noise. It also verified that the minimum description length criterion leads to models that capture the underlying dynamics of the time series, with the residual vector resembling Li.d noise. In the case of the "worst" model (largest description length), the residual vector could be distinguished from Li.d noise, confirming that it is not the "best" model. The residual vector of the "best" model (smallest description length), resembled Li.d noise, confirming that the minimum description length criterion selects a model that captures the underlying dynamics of the time series. These applications were illustrated through analysis and modelling of three time series: a time series generated by the Lorenz equations, a time series generated by electroencephalograhpic signal (EEG), and a series representing the percentage change in the daily closing price of the S&P500 index.
AFRIKAANSE OPSOMMING: In hierdie studie ondersoek ons nie-lineere modelleringstegnieke soos toegepas op dinamiese sisteme. Spesifieke aandag word geskenk aan die Metode van Surrogaat Data en die moontlikhede van hierdie metode. Binne die veld van nie-lineere modellering het ons die volgende terreine ondersoek: attraktor rekonstruksie, algemene modelleringstegnieke, kostefunksies, beskrywingslengte, en 'n spesifieke modelleringsalgoritme. Die Metode and Surrogaat Data is eerstens vir 'n meer algemene toepassing gebruik wat die gekose tydsreeks vir aanduidings van nie-lineere, dimanise struktuur toets. Tweedens, is dit vir 'n minder algemene toepassing gebruik wat die residuvektore van 'n nie-lineere model toets vir lidmaatskap van identiese en onafhanlike verspreide geraas. Die studie illustreer die noodsaaklikheid van die aanvanklike surrogaat analise van 'n tydsreeks, wat bepaal of die struktuur van die tydsreeks toegeskryf kan word aan nie-lineere, dalk chaotiese gedrag. Ons bevesting dat die weglating van hierdie analise tot foutiewelike resultate kan lei. Indien bewyse van nie-lineere gedrag in die tydsreeks gevind is, is 'n model van radiale basisfunksies gebou, deur gebruik te maak van gesofistikeerde programmatuur gebaseer op 'n spesifieke modelleringsmetodologie. Dit is 'n iteratiewe algoritme wat minimum beskrywingslengte as die termineringsmaatstaf gebruik. Die model se residuvektore is getoets vir lidmaatskap van die dinamiese klas wat as identiese en onafhanlike verspreide geraas bekend staan. Die studie verifieer dat die minimum beskrywingslengte as termineringsmaatstaf weI aanleiding tot modelle wat die onderliggende dinamika van die tydsreeks vasvang, met die ooreenstemmende residuvektor wat nie onderskei kan word van indentiese en onafhanklike verspreide geraas nie. In die geval van die "swakste" model (grootse beskrywingslengte), het die surrogaat analise gefaal omrede die residuvektor van indentiese en onafhanklike verspreide geraas onderskei kon word. Die residuvektor van die "beste" model (kleinste beskrywingslengte), kon nie van indentiese en onafhanklike verspreide geraas onderskei word nie en bevestig ons aanname. Hierdie toepassings is aan die hand van drie tydsreekse geillustreer: 'n tydsreeks wat deur die Lorenz vergelykings gegenereer is, 'n tydsreeks wat 'n elektroenkefalogram voorstel en derdens, 'n tydsreeks wat die persentasie verandering van die S&P500 indeks se daaglikse sluitingsprys voorstel.
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Rejoub, Riad A. "Projective and non-projective systems of first order nonlinear differential equations." Scholarly Commons, 1992. https://scholarlycommons.pacific.edu/uop_etds/2228.

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It is well established that many physical and chemical phenomena such as those in chemical reaction kinetics, laser cavities, rotating fluids, and in plasmas and in solid state physics are governed by nonlinear differential equations whose solutions are of variable character and even may lack regularities. Such systems are usually first studied qualitatively by examining their temporal behavior near singular points of their phase portrait. In this work we will be concerned with systems governed by the time evolution equations [see PDF for mathematical formulas] The xi may generally be considered to be concentrations of species in a chemical reaction, in which case the k's are rate constants. In some cases the xi may be considered to be position and momentum variables in a mechanical system. We will divide the equations into two classes: those in which the evolution can be carried out by the action of one of Lie's transformation groups of the plane, and those for which this is not possible. Members of the first class can be integrated by quadrature either directly or by use of an integrating factor; those in the second class cannot. Of those in the first class the most interesting evolve by transformations of the projective group, and these, as well as the equations that cannot be integrated by quadrature, we study in some detail. We seek a qualitative analysis of systems which have no linear terms in their evolution equations when the origin from which the xi are measured is a critical point. The standard, linear, phase plane analysis is of course not adequate for our purposes.
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O'Bannon, Terry Robert. "A comparison of interpolative methods for cell mapping analyses of nonlinear systems." Thesis, Georgia Institute of Technology, 1988. http://hdl.handle.net/1853/16394.

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Li, Jian. "Three dimensional isoparametric finite element analysis with geometric and material nonlinearities." Thesis, Georgia Institute of Technology, 1988. http://hdl.handle.net/1853/12165.

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Liu, Xing. "Rigorous exponential asymptotics for a nonlinear third order difference equation." Connect to this title online, 2004. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1101927781.

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Thesis (Ph. D.)--Ohio State University, 2004.
Title from first page of PDF file. Document formatted into pages; contains viii, 140 p.; also includes graphics. Includes bibliographical references (p. 139-140).
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Books on the topic "Manifolds (Mathematics) Nonlinear theories"

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V, Mikiti͡u︡k I., ed. Algebraic integrability of nonlinear dynamical systems on manifolds: Classical and quantum aspects. Dordrecht: Kluwer Academic Press, 1998.

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Li, Charles. Invariant Manifolds and Fibrations for Perturbed Nonlinear Schrödinger Equations. New York, NY: Springer New York, 1997.

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Nonlinear analysis on manifolds: Sobolev spaces and inequalities. New York, N.Y: Courant Institute of Mathematical Sciences, 2000.

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Hebey, Emmanuel. Nonlinear analysis on manifolds: Sobolev spaces and inequalities. New York: Courant Institute of Mathematical Sciences, New York University, 1999.

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Southeast Geometry Seminar (15th 2009 University of Alabama at Birmingham). Geometric analysis, mathematical relativity, and nonlinear partial differential equations: Southeast Geometry Seminars Emory University, Georgia Institute of Technology, University of Alabama, Birmingham, and the University of Tennessee, 2009-2011. Edited by Ghomi Mohammad 1969-. Providence, Rhode Island: American Mathematical Society, 2013.

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Stephen, Wiggins, ed. Invariant manifolds and fibrations for perturbed nonlinear Schrödinger equations. New York: Springer, 1997.

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Tanizaki, Hisashi. Nonlinear filters: Estimation and applications. 2nd ed. Berlin: Springer, 1996.

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Tanizaki, Hisashi. Nonlinear filters: Estimation and applications. Berlin: Springer-Verlag, 1993.

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1961-, Aston Philip J., ed. Nonlinear mathematics and its applications: Proceedings of the EPSRC Postgraduate School in Applied Nonlinear Mathematics, University of Surrey, 1995. New York: Cambridge University Press, 1996.

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Maksudov, Faramaz Gazanfar ogly. Abstracts of mathematics: Selected topics. Baku: ELM, 1999.

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Book chapters on the topic "Manifolds (Mathematics) Nonlinear theories"

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Sobolev, V. A. "Nonlocal integral manifolds and decoupling of nonlinear parabolic systems." In Lecture Notes in Mathematics, 101–8. Berlin, Heidelberg: Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/bfb0085949.

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Riaza, Ricardo. "Normal Hyperbolicity of Manifolds of Equilibria in Nonlinear Circuits with Mem-Devices." In Mathematics in Industry, 5–10. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-05365-3_1.

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Schechter, Eric. "A survey of local existence theories for abstract nonlinear initial value problems." In Lecture Notes in Mathematics, 136–84. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/bfb0086759.

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Sugimoto, Nobumasa, and Dai Shimizu. "Linear and Nonlinear Theories for Thermoacoustic Waves in a Gas Filled Tube Subject to a Temperature Gradient." In Applied Wave Mathematics II, 187–204. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-29951-4_9.

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You, Yuncheng. "Inertial Manifolds and Stabilization in Nonlinear Elastic Systems with Structural Damping." In Mathematics in Science and Engineering, 335–46. Elsevier, 1993. http://dx.doi.org/10.1016/s0076-5392(08)62393-0.

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